I am a 3rd year student at Mintlaw Academy in Scotland, and the question goes as follows;
The length of a rectangle is three times it's breadth. If the length were 6 meters less, and the breadth were 6 meters more, the rectangle would be a square. Make a mathematical model and solve the resulting equation to find the breadth of the original rectangle. What is the area of the square?
Your help would be much appreciated.
You first need to introduce some notation so suppose that the length is L and the breadth is B. The first statement "The length of a rectangle is three times it's breadth." then becomes
Now you want to form a new rectangle with the length 6 meters less, that is with lenght L - 6 and breadth six meters more, that is B + 6. This rectangle is in fact a square so its length is equal to its breadth. Thus
You should now be able to solve these two equations to find L and B. When you do so make sure you go back to the problem and verify that your solution is correct.